Phy 212: General Physics II Chapter 34: Images Lecture Notes Geometrical (Ray) Optics Geometrical Optics is an approximate treatment o light waves as straight lines (rays) or the description o image ormation 1. Light is a radiant, transverse, electromagnetic in nature wave light waves, propagating in a uniorm medium, expand equally in all directions 2. The travel o light can be approximated by rays that point normal to the plane o a traveling waveront wave source ray 1
Images An image is a visual reproduction o an object derived rom light. In geometrical optics, images are ormed where light rays intersect. Types o Images: 1. Real: these images actually exist and can be ormed and observed on a physical surace The projector image on the drymarker board is a real image 2. Virtual: these images only exist in the mind, a consequence o perception. Your image in a plane mirror is a virtual image Spherical Mirrors 1. Focal Points: the ocal point or a spherical mirror is the location along the optical axis where an object at will orm an image 1 2. Relation between mirror radius (r) & ocal point (): = 2r 3. Image ormation: 1 + 1 = 1 p i Concave Convex p i p i 2
Thin es 1. For a lens where the radii o curvature o each ace is much greater than the lens thickness, the ocal length can be calculated using the maker s ormula: 1 1 1 = ( n - 1 ) + r1 r2 Where: a. n is the index o reraction o the lens b. r 1 is the inner radius o curvature c. r 2 is the outer radius o curvature 2. The ocal length can also be calculated rom the locations o an object and its ormed image using the thin lens equation: = + p i 3. Characteristics o thin lens image ormation: a. Converging lenses (+): Image is real & inverted when p > Image is virtual & upright when p < b. Diverging lenses (-): Image is always virtual & upright Ray Diagrams or Systems 1. Converging es: 2. Diverging es: 3
Optical Instruments: Simple Magniying Glass 1. Consists o a single converging lens 2. The object is located inside ocal point 3. The inal image is virtual & upright 4. Magniication: Example: A 2 System Consider the ollowing 2 lens system: Object (h o =0.5m) L=0.30m p=20m 1 ( L1 =+0.45m) 2 ( L1 =0.05m) 1. What is the image position due to lens 1 w/r to lens 1? 2. What is the inal image position w/r to lens 2? 3. What is the inal image orientation and size? 4. What is the angular magniication o the inal image? 4
Optical Instruments: Compound Microscope 1. The object is located outside the 1 st (objective) lens 2. The converging (objective) lens orms a magniied real image inside the ocal point o a 2 nd converging (occular) lens 3. The occular lens orms a urther magniied virtual image Observed Magniication: 1 (objective) s x nearpoint m net =mlateralm θ=- objective occular 2 (occular) s Real Image Virtual Image Optical Instruments: Telescope 1. Useul or observing an object located at ininity 2. A converging (objective) lens gathers light & orms a smaller real image at the ocal point o a 2 nd (occular) lens 3. The smaller inal image ormed by the converging (occular) lens is also located at ininity but appears enlarged Angular Magniication: m θ=- objective occular 1 (objective) 2 (occular) Final Image @ Real Image 5
The Human Eye The human eye is a dynamic optical device that adjusts its ocal length to keep the image location positioned at the retina: Optical Axis Eective lens Retina 1.8 cm Optical Axis Optics o the Eye 1. The normal eye can be modeled as a simple lens system with an eective ocal length (& optical power) and a ixed image distance, i: = + p 0.018m 2. The job o the eye is to ocus images on the retina. The image distance is thereore ixed at 1.8 cm (or 0.018 m). 3. When the eye cannot adequately ocus an image on the retina, correction may be needed 4. The 4 common vision problems: a. Myopia (near sightedness, short ar & near point) b. Hypermetropia (ar sightedness, long ar & near point) c. Astigmatism (warped lens optics, ocal length not uniorm on all axes in the eye) d. Presbyopia (normal distance vision but inability to accommodate or close objects) 6
Distance Vision Optics 1. When viewing distant objects, the lens power o the eye (& ocal length) o the eye is given by: 1-1 = + = = 55.6 m 0.018 m 0.018 m 2. The lens power is 55.6 diopters & the ocal length is: = 0.018 m 3. When a person is near sighted (myopic), he/she cannot see objects at ininity ( ininity is the ar point or a normal eye) Myopic ar point < Normal ar point Example: A person with -2.0 diopter distance correction. a. This person has a lens power o 57.6 & needs this minus correction to lower the eective lens power to a normal 55.6: = + = 57.6 diopters p = 0.49 m p 0.018 m b. The ar point or this person is: p = 0.49 m {any object beyond this distance is not in ocus} Near Vision Optics 1. When viewing close-in objects, the lens power o the eye (& ocal length) o the eye is given by: -1 = + = 59.6 m 0.25 m 0.018 m 2. The lens power is 59.6 diopters & the ocal length is: = 0.0168 m 3. A ar sighted (hypermetropic) person cannot see objects at close distances even though the eye is accomodating normally Hypermetropic near point > Normal near point (0.25 m) Example: A person with +2.0 diopter vision correction. a. This person has a (near) lens power o 57.6 & needs this plus correction to raise the eective lens power to a normal close distance power o 59.6: = + = 57.6 diopters p = 0.49 m p 0.018 m b. The near point or this person is: p = 0.49 m {any object closer is not in ocus} c. People w/ presbyopia have normal distance lens power but are unable to adjust or closer objects, thus needing reader glasses 7